A $N(0,1)/(\chi^2/k)$ variable is distributed over a $t$-distribution with $k$ df.
What is an $N(a,1)/(\chi^2/k)$ variable ( $a \neq 0$) distributed as?
And am I correct in saying that the power of a $t$-test -
$\operatorname{Pr}((X - h)/(s^2/n) > T$ given that true mean = $\mu$), $h$ = hypothesis mean and $\mu$ = $h$ + q.
is determined by the above distribution? That is, is $((X-h)-\mu)/(s^2/n)$ an $N(a,1)/(\chi^2/k)$ variable?